Flaneur in the rain - iii

Suppose you're sauntering about Saint-Germain, Paris, from one cafe to the next, staying only as long as it takes you to knock down a few Brilliant problems. You're wrapping up at Brasserie Lipp and want to go to Cafè de Flore, which is across the street.

The only problem is: it's pouring rain!

If you want to absorb as little water as possible, how quickly should you run across the road?

Assumptions

Approximate yourself as a shape with a vertical cross section of \(A_\text{head}\), and horizontal cross section \(A_\text{body} \).